Multiple sources of geophysical data have been used for estimating reservoir parameters for many decades. Current approaches for geophysical inverse problems are primarily deterministic inversion methods, such as Gauss-Newton methods, conjugate gradient methods, and steepest decent techniques. These conventional methods have been successfully used to solve a wide range of complex inverse problems with tens of millions of unknowns. However, the solutions obtained using these conventional methods often depend on the choice of initial values and thus are local rather than global. In addition, the deterministic inversion methods provide very limited uncertainty information on the estimated parameters.
Stochastic inversion methods have been recognized recently as a powerful approach for solving geophysical inverse problems. Stochastic methods have several benefits over deterministic inversion methods. For example, stochastic inversion methods can provide extensive information about unknown parameters. In addition, in stochastic inversion methods, the inversion results are almost independent of initial values and therefore global and robust.